EduSahara™ Worksheet

Question 1

1.

The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 85 m, find the height of the building .

(i)

46.07 m
(ii)

52.07 m
(iii)

49.07 m
(iv)

54.07 m
(v)

44.07 m

Question 2

2.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 160 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the height of the other temple.

(i)

64.62 m
(ii)

62.62 m
(iii)

67.62 m
(iv)

72.62 m
(v)

70.62 m

Question 3

3.

A man in a boat rowing away from a lighthouse 35 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.

(i)

8.27 m/sec
(ii)

0.27 m/sec
(iii)

1.27 m/sec
(iv)

7.27 m/sec
(v)

2.27 m/sec

Question 4

4.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?

(i)

∠d
(ii)

∠b
(iii)

∠e
(iv)

∠c

Question 5

5.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 17 m, find the height of the flag staff .

(i)

12.45 m
(ii)

17.45 m
(iii)

7.45 m
(iv)

15.45 m
(v)

9.45 m

Question 6

6.

From the top of a light house which is 90 m high from the sea level, the angles of depression of two ships are 60° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

127.91 m
(ii)

98.91 m
(iii)

103.91 m
(iv)

91.91 m
(v)

119.91 m

Question 7

7.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the distance between the point and the top of the
radio tower
is
160 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

82

m
(ii)

81

m
(iii)

79

m
(iv)

77

m
(v)

80

m

Question 8

8.

From the top of a 10 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.

(i)

43.00 m
(ii)

35.00 m
(iii)

37.00 m
(iv)

45.00 m
(v)

40.00 m

Question 9

9.

The angles of depression of two boats from the top of a cliff 180 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

397.71 m
(ii)

428.71 m
(iii)

431.71 m
(iv)

415.71 m

Question 10

10.

The angles of depression of two boats from the top of a cliff 120 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

87.85 m
(ii)

82.85 m
(iii)

92.85 m
(iv)

84.85 m
(v)

90.85 m

Question 11

11.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the height of the
chimney
is
80 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

160

m
(ii)

80

m
(iii)

40

√

12

m
(iv)

80

√

2

m
(v)

160

√

3

m

Question 12

12.

From a point 190 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the cliff.

(i)

187.00 m
(ii)

166.00 m
(iii)

207.00 m
(iv)

190.00 m
(v)

198.00 m

Question 13

13.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠d
(ii)

∠a
(iii)

∠b
(iv)

∠c

Question 14

14.

The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .

(i)

17.99 m
(ii)

9.99 m
(iii)

7.99 m
(iv)

15.99 m
(v)

12.99 m

Question 15

15.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 90 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

331.89 m
(ii)

343.89 m
(iii)

350.89 m
(iv)

335.89 m
(v)

308.89 m

Question 16

16.

From a point 150 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the pillar.

(i)

58.39 m
(ii)

60.39 m
(iii)

68.39 m
(iv)

66.39 m
(v)

63.39 m

Question 17

17.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 8 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?

(i)

7 min 54 sec
(ii)

10 min 56 sec
(iii)

11 min 57 sec
(iv)

12 min 58 sec
(v)

9 min 55 sec

Question 18

18.

A
tower
stands vertically on the ground.

The height of the
tower
is
10

√

2

m
.

The distance between the observation point and its top
is
20

m
.

Find the angle of elevation.

(i)

60°
(ii)

30°
(iii)

75°
(iv)

45°
(v)

105°

Question 19

19.

A flagstaff stands on the top of a building at a distance of 10 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

20
3

√

3

m
(ii)

20

m
(iii)

10

√

2

m
(iv)

20
3

m
(v)

20
3

√

18

m

Question 20

20.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 16 m, find the height of the building .

(i)

7.00 m
(ii)

6.00 m
(iii)

9.00 m
(iv)

8.00 m
(v)

10.00 m

Question 21

21.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 160 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the width of the river .

(i)

89.37 m
(ii)

97.37 m
(iii)

92.37 m
(iv)

95.37 m
(v)

87.37 m

Question 22

22.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the distance between the point and the top of the
chimney
is
170 m
,
find the height of the
chimney
.

(i)

85

√

2

m
(ii)

85

m
(iii)

170

√

3

m
(iv)

170

m
(v)

85
2

√

12

m

Question 23

23.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
30°
.
If the height of the
chimney
is
110 m
,
find the distance between
the observation point and the foot of the
chimney
.

(i)

110

m
(ii)

110

√

3

m
(iii)

165

√

2

m
(iv)

330

m
(v)

110

√

18

m

Question 24

24.

Two boys are on opposite sides of a tower of 80 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.

(i)

(

80
3

√

3

+

80

)

m
(ii)

(

80
3

√

18

+

80

√

6

)

m
(iii)

(

40

√

2

+

40

√

6

)

m
(iv)

(

−

2

−

√

3

)

m
(v)

(

−

12800
3

)

m

Question 25

25.

A man 1.4 m tall stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.9 m on the ground. Find the height of the lamp post .

(i)

1.31 m
(ii)

4.31 m
(iii)

0.31 m
(iv)

2.31 m
(v)

3.31 m

Assignment Key